Details

analyze383.0ms (16.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample928.0ms (40.4%)

Symmetry

(sort x y)

Results

847.0ms	8256×	body	128	valid
43.0ms	482×	body	128	invalid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
5×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	17	15
2	34	11
3	57	11
4	75	11
5	81	11

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 42 computations (50% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (.f64 z (.f64 z 3)))
✓	0.2b	(.f64 z (.f64 z 3))

series14.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(fma.f64 x y (.f64 z (.f64 z 3)))
2.0ms	(.f64 z (.f64 z 3))

rewrite40.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`log1p-expm1-u_binary64`
680×	`expm1-log1p-u_binary64`
200×	`prod-diff_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	160	18
2	1860	18

Stop Event

1×	node limit

Counts

2 → 38

Calls

2 calls:

39.0ms	(fma.f64 x y (.f64 z (.f64 z 3)))
39.0ms	(.f64 z (.f64 z 3))

simplify76.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

605×	`sqr-pow_binary64`
443×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	429
1	19	429
2	33	429
3	57	429
4	119	429
5	320	429
6	1229	429
7	2130	429
8	2294	429
9	2478	429
10	2686	429
11	2978	429
12	3369	429
13	3849	429
14	4408	429

Stop Event

1×	node limit

Counts

86 → 43

prune33.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	38	5	43
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	39	6	45

Error

0.0b

Counts

45 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
	19.1b	(fma.f64 x y (cbrt.f64 (pow.f64 (.f64 z (.f64 z 3)) 3)))
	0.3b	(fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 3)) 2))
	0.6b	(fma.f64 x y (pow.f64 (cbrt.f64 (.f64 z (.f64 z 3))) 3))
▶	0.1b	(fma.f64 3 (.f64 z z) (.f64 y x))
	19.6b	(pow.f64 (sqrt.f64 (fma.f64 x y (.f64 z (.f64 z 3)))) 2)

Compiler

Compiled 662 to 412 computations (37.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3 (.f64 z z) (.f64 y x))

series10.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(fma.f64 3 (*.f64 z z) (*.f64 y x))

rewrite37.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`log1p-expm1-u_binary64`
652×	`expm1-log1p-u_binary64`
139×	`expm1-udef_binary64`
139×	`log1p-udef_binary64`
131×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	159	11
2	1821	11

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

37.0ms

(fma.f64 3 (*.f64 z z) (*.f64 y x))

simplify69.0ms (3%)

Algorithm

1×	egg-herbie

Rules

606×	`sqr-pow_binary64`
444×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	345
1	19	345
2	33	345
3	58	345
4	122	345
5	362	345
6	1266	345
7	2167	345
8	2331	345
9	2515	345
10	2723	345
11	3014	345
12	3407	345
13	3885	345
14	4446	345

Stop Event

1×	node limit

Counts

62 → 31

prune23.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	31	6	37

Error

0.0b

Counts

37 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
	19.1b	(fma.f64 x y (cbrt.f64 (pow.f64 (.f64 z (.f64 z 3)) 3)))
▶	0.3b	(fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 3)) 2))
	0.6b	(fma.f64 x y (pow.f64 (cbrt.f64 (.f64 z (.f64 z 3))) 3))
✓	0.1b	(fma.f64 3 (.f64 z z) (.f64 y x))
	19.6b	(pow.f64 (sqrt.f64 (fma.f64 x y (.f64 z (.f64 z 3)))) 2)

Compiler

Compiled 522 to 271 computations (48.1% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 3)) 2))
✓	0.3b	(pow.f64 (*.f64 z (sqrt.f64 3)) 2)
✓	0.4b	(*.f64 z (sqrt.f64 3))

series28.0ms (1.2%)

Counts

3 → 60

Calls

3 calls:

20.0ms	(fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 3)) 2))
5.0ms	(pow.f64 (*.f64 z (sqrt.f64 3)) 2)
3.0ms	(*.f64 z (sqrt.f64 3))

rewrite47.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`log1p-expm1-u_binary64`
776×	`expm1-log1p-u_binary64`
170×	`prod-diff_binary64`
94×	`add-sqr-sqrt_binary64`
89×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	205	24
2	2215	24

Stop Event

1×	node limit

Counts

3 → 64

Calls

3 calls:

46.0ms	(fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 3)) 2))
46.0ms	(pow.f64 (*.f64 z (sqrt.f64 3)) 2)
46.0ms	(*.f64 z (sqrt.f64 3))

simplify95.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-l_binary64`
538×	`sqr-pow_binary64`
468×	`associate-r_binary64`
438×	`*-commutative_binary64`
258×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	716
1	28	501
2	50	501
3	112	501
4	410	501
5	2104	501
6	2271	501
7	2471	501
8	2668	501
9	2899	501
10	3204	501
11	3845	501
12	4320	501
13	4943	501

Stop Event

1×	node limit

Counts

124 → 72

prune60.0ms (2.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	71	7	78

Error

Counts

78 → 7

Alt Table

Status	Error	Program
▶	0.4b	(fma.f64 x y (*.f64 (pow.f64 (sqrt.f64 3) 2) (pow.f64 z 2)))
✓	0.1b	(fma.f64 3 (.f64 z z) (.f64 y x))
	13.5b	(fma.f64 x y (.f64 (cbrt.f64 (.f64 3 (.f64 z z))) (cbrt.f64 (pow.f64 (.f64 z (sqrt.f64 3)) 4))))
✓	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
✓	0.3b	(fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 3)) 2))
	0.6b	(fma.f64 x y (pow.f64 (cbrt.f64 (.f64 z (.f64 z 3))) 3))
	19.6b	(pow.f64 (sqrt.f64 (fma.f64 x y (.f64 z (.f64 z 3)))) 2)

Compiler

Compiled 1055 to 658 computations (37.6% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 (pow.f64 (sqrt.f64 3) 2) (pow.f64 z 2)))
✓	0.2b	(*.f64 (pow.f64 (sqrt.f64 3) 2) (pow.f64 z 2))
✓	1.0b	(pow.f64 (sqrt.f64 3) 2)

series26.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

19.0ms	(fma.f64 x y (*.f64 (pow.f64 (sqrt.f64 3) 2) (pow.f64 z 2)))
6.0ms	(*.f64 (pow.f64 (sqrt.f64 3) 2) (pow.f64 z 2))
0.0ms	(pow.f64 (sqrt.f64 3) 2)

rewrite42.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

772×	`log1p-expm1-u_binary64`
772×	`expm1-log1p-u_binary64`
136×	`prod-diff_binary64`
96×	`add-sqr-sqrt_binary64`
92×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	226	19
2	2232	19

Stop Event

1×	node limit

Counts

3 → 38

Calls

3 calls:

42.0ms	(fma.f64 x y (*.f64 (pow.f64 (sqrt.f64 3) 2) (pow.f64 z 2)))
42.0ms	(*.f64 (pow.f64 (sqrt.f64 3) 2) (pow.f64 z 2))
42.0ms	(pow.f64 (sqrt.f64 3) 2)

simplify82.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-l_binary64`
538×	`sqr-pow_binary64`
470×	`*-commutative_binary64`
453×	`associate-r_binary64`
258×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	500
1	24	345
2	49	345
3	116	345
4	417	345
5	2084	345
6	2251	345
7	2449	345
8	2646	345
9	2879	345
10	3182	345
11	3855	345
12	4330	345
13	4953	345

Stop Event

1×	node limit

Counts

74 → 43

prune31.0ms (1.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	43	7	50

Error

Counts

50 → 7

Alt Table

Status	Error	Program
	13.4b	(fma.f64 x y (sqrt.f64 (*.f64 9 (pow.f64 z 4))))
✓	0.1b	(fma.f64 x y (.f64 z (.f64 z 3)))
✓	0.4b	(fma.f64 x y (*.f64 (pow.f64 (sqrt.f64 3) 2) (pow.f64 z 2)))
✓	0.1b	(fma.f64 3 (.f64 z z) (.f64 y x))
✓	0.3b	(fma.f64 x y (pow.f64 (*.f64 z (sqrt.f64 3)) 2))
	0.6b	(fma.f64 x y (pow.f64 (cbrt.f64 (.f64 z (.f64 z 3))) 3))
	19.6b	(pow.f64 (sqrt.f64 (fma.f64 x y (.f64 z (.f64 z 3)))) 2)

Compiler

Compiled 596 to 335 computations (43.8% saved)

regimes132.0ms (5.7%)

Accuracy

Total 0.1b remaining (92%)

Threshold costs 0.1b (92%)

Counts

21 → 1

Compiler

Compiled 1718 to 1197 computations (30.3% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11

Stop Event

1×

saturated

end92.0ms (4%)

Remove: (sort x y)
Compiler: Compiled 132 to 91 computations (31.1% saved)

Details

analyze383.0ms (16.7%)

sample928.0ms (40.4%)

simplify13.0ms (0.6%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.6%)

rewrite40.0ms (1.7%)

simplify76.0ms (3.3%)

prune33.0ms (1.5%)

localize5.0ms (0.2%)

series10.0ms (0.5%)

rewrite37.0ms (1.6%)

simplify69.0ms (3%)

prune23.0ms (1%)

localize7.0ms (0.3%)

series28.0ms (1.2%)

rewrite47.0ms (2.1%)

simplify95.0ms (4.1%)

prune60.0ms (2.6%)

localize10.0ms (0.4%)

series26.0ms (1.1%)

rewrite42.0ms (1.8%)

simplify82.0ms (3.6%)

prune31.0ms (1.4%)

regimes132.0ms (5.7%)

simplify3.0ms (0.2%)

end92.0ms (4%)

Profiling